The electrical power supplied by a multiphase AC source to the stator windings of an asynchronous rotary machine serves to magnetize the machine by generating both stator flux .PHI..sub.S and rotor flux .PHI..sub.R therein, and more particularly it serves to create electromagnetic torque .GAMMA. therein.
With asynchronous rotary machines it is conventional to make use of stator flux control since that makes it possible in particular to keep a machine in motor operation within the limits within which its electromagnetic state is the best possible, consequently giving rise to the highest efficiency in terms of converting received electrical energy into mechanical energy.
Naturally, it is essential to have full control over torque output for a machine that is operating as a motor.
In conventional manner, the Concordia transform makes it possible by means of two independent components V.sub.S.alpha. and V.sub.S.beta. to define the power supply voltage V.sub.S applied to the stator of a three-phase motor in which neutral is not distributed.
A known control method is described in particular in document EP-A-0812059. It relates to an n-phase rotary machine powered by means of a voltage inverter having n switches with m states, and known as a single-pole m-logic level (SPmLL) machine, that enables m.sup.n distinct output states to be obtained, and thus in the present case makes it possible to obtain m.sup.n distinct stator power supply voltages for the machine, each of said voltages being conventionally represented by a vector at a given instant. A servo-control system is implemented so that the multi-state switches change state in such a manner as to define a power supply vector that is optimum at all times and so as to bring the torque .GAMMA. and the stator flux .PHI..sub.S of the machine towards the reference torque and the reference flux as already defined. That servo-control system has a set of sensors, an observer, and a computer. The computer controls selection of the optimum power supply vector by acting selectively on the switches. The rotation of the stator power supply voltage vector V.sub.S of a machine in operation gives rise to the selection being varied over time. Thus, for a three-phase inverter including a two-state switch, i.e. two logic states per phase, selection is performed amongst eight vectors corresponding to the 2.sup.3 logical combinations (or output states) of the inverter, which are shown diagrammatically in FIG. 1, two of them being of zero amplitude and corresponding to the cases of all of the switches being open or all of the switches being closed, in conventional manner.
As a consequence of the above, the working space in which the methods of document EP-A-0812059 and of the invention are implemented, is the (.PHI..sub.S.alpha., .PHI..sub.S.beta., .GAMMA.) domain which can be subdivided into two sub-spaces, one of which is constituted by the (.PHI..sub.S.alpha., .PHI..sub.S.beta.) plane and the other by variation over time in the torque (.GAMMA., t).
The purpose of the servo-control is to achieve direct control over the torque .GAMMA. and over the stator flux amplitude .vertline..PHI..sub.S.vertline. as a function of reference values for flux and torque given respectively by .vertline..PHI..sub.S.vertline..sub.ref and .GAMMA..sub.ref. These references can be translated into the (.PHI..sub.S.alpha., .PHI..sub.S.beta., .GAMMA.) domain in a geometrical form as shown diagrammatically in FIG. 2 where there is shown a three-dimensional frame of reference having a vertical axis which is assumed to be graduated in torque values .GAMMA., and two horizontal axes .PHI..sub.S.alpha. and .PHI..sub.S.beta. which are graduated in flux values.
The path of the reference flux .PHI..sub.Sref corresponds to a rotating field, and the vertical cylinder centered on the torque axis .GAMMA. on the frame of reference represents the reference flux:
the reference torque in this case is assumed to be located on the horizontal reference plane (.PHI..sub.S.alpha., .PHI..sub.S.beta.) associated with the torque value graduation on the vertical axis corresponding to the torque .GAMMA..sub.ref ; and
the horizontal circle where the horizontal plane at altitude .GAMMA..sub.ref intersects the cylinder corresponds to the reference (.vertline..PHI..sub.S.vertline..sub.ref, .GAMMA..sub.ref).
The purpose of servo-control is to reproduce the trajectory defined by this circle of intersection by controlling the inverter appropriately, making best use of the means constituted by the switches, while keeping as close as possible to the reference torque value. It is not possible to follow the ideal trajectory in three dimensions accurately insofar as the number of different output voltage vectors which an inverter can produce is limited.
Thus, starting from a point A that is representative of a current state corresponding to a flux level and to a torque level at a given instant in the operation of a machine, as shown in FIG. 2, the purpose of the control system is to control the inverter in such a manner as to attempt to reach a point such a D which is situated on the circle of intersection, and to do so within a determined time interval, for example equal to 1/(2f.sub.d), where f.sub.d is the chopper frequency of the inverter.
Because of the small number of output voltage vectors available from an inverter, it is necessary to implement a plurality of different commands during a single time interval in order to obtain the above-indicated results, as represented in FIG. 2 by the three vectors AB, BC, CD, each of which corresponds to an output voltage of the inverter, and thus from the stator power supply V.sub.S.
The computer in the servo-control system makes use of an algorithm that makes it possible to select an optimum sequence for controlling the inverter during each of the successive time intervals subdividing the operating time of the machine, on the basis of values supplied by the servo-control system sensors and reference values concerning flux and torque.
In particular, provision is made in the above-mentioned European document, for each sequence to extend over a time interval equal to 1/(2f.sub.d) and to comprise three distinct inverter commands which are implemented in succession and each of which corresponds to a different stator voltage vector V.sub.S. The first two commands are active and cause the motor torque to vary in a manner that corresponds to acceleration or deceleration of the rotating vector corresponding to the stator flux .PHI..sub.S relative to the rotating vector corresponding to the rotor flux .PHI..sub.R, while the third command is passive and allows the torque to reduce, corresponding to the stator flux vector catching up the rotor flux vector.
The search performed during each time interval for the optimum sequence seeks to determine the sole triplet of commands having respective positive durations that make it possible to reach a point on the above-mentioned circle of intersection within the available time interval. This search for an optimum sequence can be unsuccessful in the event of large transients, in which case a more suitable strategy is used, as described in detail in the above-mentioned European document EP-A-0812059.
In conventional manner, the calculation required for determining the command triplets, and more particularly the durations during which each command stage should be implemented, are themselves complex and require expensive investment in software and hardware.
At the beginning of each cycle of seeking an optimum sequence, the algorithm used by the computer selects the sole triplet of commands having positive duration that makes it possible to reach the circle of intersection at the end of a time interval 1/(2f.sub.d).
In a first step corresponding to the vector AB in FIGS. 2 to 4, it is necessary to perform calculation for the point A and for all current points A' following A along the vector AB and corresponding to successive samples. These calculations seek to determine the remaining conduction times dt.sub.1, dt.sub.2, and dt.sub.3 for application of each of the three commands provided in the sequence on the basis of the following equations, where t is current time: EQU dt.sub.1 +dt.sub.2 +dt.sub.3 =1/(2f.sub.d)-t EQU .GAMMA./(2f.sub.d)=.GAMMA..sub.ref EQU .PHI..sub.S.sup.2 /(2f.sub.d)=.PHI..sub.Sref.sup.2
This system of three equations in three unknowns is linearized about the operating point, and since the equation of a cylinder is quadratic, it is possible to replace the cylinder target D as shown in FIG. 2 by a plane target that is tangential to the current arrival point D'.
The resulting equation 1 is written as follows: ##EQU2##
it provides the three durations of application for an optimum sequence, plus the parameter .lambda. which defines the end point D of a sequence on the tangent to the circle of intersection. When calculation gives a value for dt.sub.2 that is less than the sampling period T, the instant at which switchover occurs from the first step to the second step can take place, with said instant corresponding to point B in FIGS. 2 to 4.
In a second active command stage, corresponding to vector BC in FIGS. 2 to 4, above equation 1 needs to be solved taking account of the fact that dt.sub.2 =0, and unfortunately there is no exact solution for dt.sub.3. It is therefore necessary to use an approximate solution which minimizes error, said solution being assumed in this case to be obtained by applying the method of least squares. Equation 2 which is derived from equation 1 and taking the above-indicated elements into account serves to determine the duration dt.sub.3 of this second stage and as a consequence the duration dt.sub.1 of the last of the three stages of the sequence under consideration, and also a new value for .lambda..
When calculation gives dt.sub.3 a value that is less than the sampling period T, the instant at which the second stage switches to the third can be determined, with this instant corresponding to point C in FIGS. 2 to 4.
In a third or passive command stage, corresponding to vector CD, equation 2 as obtained from equation 1 needs to be solved while taking account of the fact that dt.sub.3 =0. That equation likewise does not give an exact solution and the least squares method is again used to provide an approximate solution.
Implementing the calculations required to operate a machine controlled by a servo-control system that implements the stages summarized above and for each of the optimized command sequences that are required in succession, implies implementing software and hardware means that, at present, can only be envisaged using machines that are themselves very expensive, such as very high power machines that are unsuitable for controlling more ordinary machines.